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Full-Text Articles in Physical Sciences and Mathematics
Whitehead Products In Function Spaces: Quillen Model Formulae, Gregory Lupton, Samuel Bruce Smith
Whitehead Products In Function Spaces: Quillen Model Formulae, Gregory Lupton, Samuel Bruce Smith
Mathematics and Statistics Faculty Publications
We study Whitehead products in the rational homotopy groups of a general component of a function space. For the component of any based map f : X→Y, in either the based or free function space, our main results express the Whitehead product directly in terms of the Quillen minimal model of f. These results follow from a purely algebraic development in the setting of chain complexes of derivations of differential graded Lie algebras, which is of interest in its own right. We apply the results to study the Whitehead length of function space components.
Anticommuting Derivations, Steen Pedersen
Anticommuting Derivations, Steen Pedersen
Mathematics and Statistics Faculty Publications
We show that the re are no non-trivial closable derivations of a C*-algebra anticommuting with an ergodic action of a compact group, supposing that the set of squares is dense in the group. We also show that the re are no non-trivial closable densely defined rank one derivations on any C*-algebra.
On The Product Of Two Generalized Derivations, Mohamed Barraa, Steen Pedersen
On The Product Of Two Generalized Derivations, Mohamed Barraa, Steen Pedersen
Mathematics and Statistics Faculty Publications
Two elements A and B in a ring R determine a generalized derivation deltaA,B on R by setting δA,B(X) = AX - XA for any X in R. We characterize when the product δC,DδA,B is a generalized derivation in the cases when the ring R is the algebra of all bounded operators on a Banach space epsilon, and when R is a C*-algebra U. We use the se characterizations to compute the commutant of the range of δA,B.